Math Quiz and Prime Factorization Concepts

Test your math knowledge with a quiz ranging from square numbers to factorization and explore prime factorization concepts through examples and practice questions involving finding prime factors, highest common factor (HCF), and lowest common multiple (LCM).

• Math
• Quiz
• Prime Factorization
• HCF
• LCM

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1. 1-10 Quiz. 1) 18 17 2) 46 4 3) 144 4) List the first 5 Square Numbers. 5) Factorise ?2+ 4? 6) What is the value of the 4 in 0.34 7) 8 8) Simplify 4? 5? 9) 0.25hrs is how many minutes? 10) Give an angle fact about quadrilaterals. 2 5+3

2. 1-10 Quiz. 1) 18 17 2) 46 4 3) 144 4) List the first 5 Square Numbers. 5) Factorise ?2+ 4? 6) What is the value of the 4 in 0.34 7) 8 8) Simplify 4? 5? 9) 0.25hrs is how many minutes? 10) Give an angle fact about quadrilaterals. 306 11.5 12 1, 4, 9, 16, 25 p (p + 4) 4/100 31/40 9e 15 minutes Angles add up to 360 2 5+3

3. Title: HCF and LCM Objectives To be able to perform a Prime Factor Decomposition. To be able to find the HCF and LCM using Venn Diagrams.

4. 2 5 3 4 1 9 8 6 7 Sort the digits 1, 2, 3, 4, 5, 6, 7, 8, 9 into the grid so that they obey the row and column headings.

5. Prime Factor Trees 36 Write 36 as a product of its prime factors. - Split the number into two factors. Circle the factors if they are Prime. If not split it down again. List as a multiplication all the numbers circled. 3 12 - 4 3 - - 2 36 = 2 2 3 3 2 = 22 32

6. Prime Factor Trees 2100 Write 2100 as a product of its prime factors. - Split the number into two factors. Circle the factors if they are Prime. If not split it down again. List as a multiplication all the numbers circled. 30 70 - 5 7 10 6 - 5 2 - 2 3 2100 = 2 2 3 5 5 7 = 22 3 52 7

7. Your Turn Write each of these numbers as the product of its prime factors. Pick a difficulty and try to complete all 4 numbers. 10 28 14 48 15 60 30 72 112 240 144 192

8. Answers 10 = 2x 5 14 = 2 x 7 15 = 3 x 5 30 = 2 x 3 x 5 28 = 2 x 7 48 = 24 x 3 60 = 2 x 3 x 5 72 = 23 x 3 112 = 24 x 7 240 = 24 x 3 x 5 144 = 24 x 3 192 = 26 x 3

9. The highest common factor (HCF) of two numbers is the highest whole number which divides into both. The lowest common multiple (LCM) of two numbers is the smallest number that is a multiple of both.

10. The easier questions The highest common factor (HCF) of two numbers is the highest whole number which divides into both. Q) Find the Highest Common Factor (HCF) of 32 and 48 Factors of 32: 1, 32, 2, 16, 4, 8 Factors of 48: 1, 48, 2, 24, 3, 16, 4, 12, 6, 8 The Highest Common Factor is 16

11. The easier questions The lowest common multiple (LCM) of two numbers is the smallest number that is a multiple of both. Q) Find the Lowest Common Multiple (LCM) of 6 and 10 Multiples of 6: 6, 12, 18, 24, 30, 36 10, 20, 30, 40 Multiples of 10: The Lowest Common Multiple is 30

12. Bronze Silver Gold 1) Find the HCF of 4 and 10. 2) Find the HCF of 9 and 15. 3) Find the LCM of 3 and 5. 4) Find the LCM of 4 and 8. 1) Find the HCF of 18 and 42. 2) Find the HCF of 14 and 32. 3) Find the LCM of 10 and 15. 4) Find the LCM of 36 and 48. 1) Find the HCF of 24 and 64. 2) Find the HCF of 81 and 150. 3) Find the LCM of 25 and 85. 4) Find the LCM of 120 and 160. Questions

13. Bronze Silver Gold 1) 2 1) 6 1) 8 2) 3 2) 2 2) 3 3) 15 3) 30 3) 425 4) 8 4) 144 4) 480 Answers

14. We can use the prime factors of a number to find the HCF and LCM of larger numbers. Example: Find the HCF and the LCM of 60 and 294 60 294 2 3 7 7 2 2 3 5 60 = 294 =

15. 294 = 2 3 7 7 60 = 2 2 3 5 60 294 2 2 7 3 7 5 HCF of 60 and 294 = 2 x 3 = 6

16. 294 = 2 3 7 7 60 = 2 2 3 5 60 294 2 2 7 3 7 5 HCF of 60 and 294 = 2 x 3 = 6 LCM of 60 and 294 = 2 x 5 x 2 x 3 x 7 x 7 = 2940

17. Your Turn Pick any 4 of the following questions to try and complete: Find the HCF and LCM of a) 12 and 20 c) 18 and 24 e) 30 and 42 b) 15 and 40 d) 7 and 12 f) 9 and 60 For each question I expect to see: - Prime Factor Decomposition for each number (2 trees) - The Venn Diagram - Answers for the HCF and LCM. As you will see on the next slides, I have done this myself for every question.

21. Common Worded Exam Questions

22. Common Worded Exam Questions 20 40 60 80 100 120 140 160 180 200 220 36 72 108 144 180 .. 180 seconds

23. Common Worded Exam Questions

24. Common Worded Exam Questions 20 40 60 80 100 120 140 160 180 200 220 15 30 45 60 .. 60 seconds

25. Todays Objectives Have you met them? Objectives To be able to perform a Prime Factor Decomposition. To be able to find the HCF and LCM using Venn Diagrams.

26. Suggested Videos For this lesson For next lesson Ordering Numbers: https://www.youtube.com/watch?v=gOmj58JdxL8 Ordering fractions decimals percentages Corbettmaths Percentages: Adding & Subtracting Fractions: https://www.youtube.com/watch?v=5juto2ze8Lg Math Antics - Adding and Subtracting Fractions Working with decimals: https://www.youtube.com/watch?v=kwh4SD1ToFc Math Antics - Decimal Arithmetic BIDMAS: https://www.youtube.com/watch?v=6K77Igo39vk GCSE Maths - BIDMAS - Aslam Tutoring